Product set growth in Burnside groups

Coulon, Rémi; Steenbock, Markus

doi:10.5802/jep.187

Product set growth in Burnside groups
[Croissance des ensembles produit dans les groupes de Burnside]

Coulon, Rémi ¹ ; Steenbock, Markus ²

¹ IRMAR, Univ Rennes et CNRS 35000 Rennes, France
² Fakultät für Mathematik, Universität Wien 1090 Wien, Austria

Journal de l’École polytechnique — Mathématiques, Tome 9 (2022), pp. 463-504.

Résumé
Abstract

Étant donné un quotient périodique d’un groupe hyperbolique sans torsion, nous donnons une estimation inférieure fine de la fonction de croissance pour chacun de tous ses sous-semi-groupes. Cet énoncé généralise des résultats de Razborov et Safin pour les groupes libres.

Given a periodic quotient of a torsion-free hyperbolic group, we provide a fine lower estimate of the growth function of any sub-semi-group. This generalizes results of Razborov and Safin for free groups.

Reçu le : 2021-02-26
Accepté le : 2022-02-15
Publié le : 2022-02-28

DOI : 10.5802/jep.187

Classification : 20F65, 20F67, 20F50, 20F06, 20F69
Keywords: Product sets, growth, hyperbolic groups, acylindrical actions, small cancellation, infinite periodic groups, Burnside problem
Mot clés : Ensemble produit, croissance, groupes hyperboliques, actions cylindriques, théorie de la petite simplification, groupes périodiques infinis, problème de Burnside

Affiliations des auteurs :

Coulon, Rémi ¹ ; Steenbock, Markus ²

¹ IRMAR, Univ Rennes et CNRS 35000 Rennes, France
² Fakultät für Mathematik, Universität Wien 1090 Wien, Austria

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Coulon, Rémi; Steenbock, Markus. Product set growth in Burnside groups. Journal de l’École polytechnique — Mathématiques, Tome 9 (2022), pp. 463-504. doi : 10.5802/jep.187. http://www.numdam.org/articles/10.5802/jep.187/

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